{"id":419,"date":"2023-06-05T15:31:07","date_gmt":"2023-06-05T15:31:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/finding-percent-increase-and-percent-decrease\/"},"modified":"2026-09-23T21:57:34","modified_gmt":"2026-09-23T21:57:34","slug":"finding-percent-increase-and-percent-decrease","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/finding-percent-increase-and-percent-decrease\/","title":{"raw":"Finding Percent Change","rendered":"Finding Percent Change"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find percent change (increase or decrease)<\/li>\r\n<\/ul>\r\n<\/div>\r\nPeople in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.\r\n\r\nTo find the percent change, first we find the amount of change, which is the difference between the new amount and the original amount. Then we find what percent the amount of change is of the original amount.\r\n<div class=\"textbox shaded\">\r\n<h3>Find Percent CHANGE<\/h3>\r\nStep 1. Find the amount of change.\r\n<ul id=\"fs-id1166490916546\">\r\n \t<li>[latex]\\text{change}=\\text{new amount}-\\text{original amount}[\/latex]<\/li>\r\n<\/ul>\r\nStep 2. Divide the amount of change found in Step 1 by the original amount (this will result in a decimal).\r\n\r\nStep 3. Convert the decimal found in Step 2 to a percentage by multiplying by 100.\u00a0 Add the percent symbol %.\r\n\r\nIf the answer is negative, the change is a decrease. The answer must include either a negative sign or the word decrease, but not both.\r\n\r\nIf the answer is positive, the change is an increase.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nIn [latex]2011[\/latex], the California governor proposed raising community college fees from [latex]\\text{\\$26}[\/latex] per unit to [latex]\\text{\\$36}[\/latex] per unit. Find the percent change. (Round to the nearest tenth of a percent.)\r\n\r\nSolution\r\n\r\n<strong>Finding Percent Change<\/strong>\r\nFind the Amount of Change: new - original = 36 - 26 = 10\r\nDivide by the Original Amount: 10\/26 =\u00a0 0.3846153846\r\nConvert to a Percent and Round: 0.3846153846 x 100 = 38.5%\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<span style=\"color: #ff0000;\"><strong>NOTE:\u00a0<span style=\"color: #000000;\">The frame around the answer will turn\u00a0red if the answer entered is wrong.<\/span><\/strong><\/span>\r\n\r\n[ohm_question]329598[\/ohm_question]\r\n\r\n[ohm_question]329599[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe average price of a gallon of gas in one city in June [latex]2014[\/latex] was [latex]\\text{\\$3.71}[\/latex]. The average price in that city in July was [latex]\\text{\\$3.64}[\/latex]. Find the percent change.\r\n[reveal-answer q=\"516647\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"516647\"]\r\n\r\nSolution\r\n\r\n<strong>Finding Percent Change<\/strong>\r\nFind the Amount of Change: new - original = 3.64 - 3.71 = [latex]-[\/latex]$0.07\r\nDivide by the Original Amount: [latex]-[\/latex]0.07\/3.71 =\u00a0 [latex]-[\/latex]0.0188679245\r\nConvert to a Percent and Round: 0.0188679245 x 100 = [latex]-[\/latex]1.9% (or 1.9% decrease)\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<span style=\"color: #ff0000;\"><strong>NOTE:\u00a0<span style=\"color: #000000;\">The frame around the answer will turn\u00a0red if the answer entered is wrong.<\/span><\/strong><\/span>\r\n\r\n[ohm_question]329600[\/ohm_question]\r\n\r\n[ohm_question]329601[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to find percent change.\r\n\r\nhttps:\/\/youtu.be\/mfe__iO5fbk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find percent change (increase or decrease)<\/li>\n<\/ul>\n<\/div>\n<p>People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.<\/p>\n<p>To find the percent change, first we find the amount of change, which is the difference between the new amount and the original amount. Then we find what percent the amount of change is of the original amount.<\/p>\n<div class=\"textbox shaded\">\n<h3>Find Percent CHANGE<\/h3>\n<p>Step 1. Find the amount of change.<\/p>\n<ul id=\"fs-id1166490916546\">\n<li>[latex]\\text{change}=\\text{new amount}-\\text{original amount}[\/latex]<\/li>\n<\/ul>\n<p>Step 2. Divide the amount of change found in Step 1 by the original amount (this will result in a decimal).<\/p>\n<p>Step 3. Convert the decimal found in Step 2 to a percentage by multiplying by 100.\u00a0 Add the percent symbol %.<\/p>\n<p>If the answer is negative, the change is a decrease. The answer must include either a negative sign or the word decrease, but not both.<\/p>\n<p>If the answer is positive, the change is an increase.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>In [latex]2011[\/latex], the California governor proposed raising community college fees from [latex]\\text{\\$26}[\/latex] per unit to [latex]\\text{\\$36}[\/latex] per unit. Find the percent change. (Round to the nearest tenth of a percent.)<\/p>\n<p>Solution<\/p>\n<p><strong>Finding Percent Change<\/strong><br \/>\nFind the Amount of Change: new &#8211; original = 36 &#8211; 26 = 10<br \/>\nDivide by the Original Amount: 10\/26 =\u00a0 0.3846153846<br \/>\nConvert to a Percent and Round: 0.3846153846 x 100 = 38.5%<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><span style=\"color: #ff0000;\"><strong>NOTE:\u00a0<span style=\"color: #000000;\">The frame around the answer will turn\u00a0red if the answer entered is wrong.<\/span><\/strong><\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm329598\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=329598&theme=oea&iframe_resize_id=ohm329598&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm329599\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=329599&theme=oea&iframe_resize_id=ohm329599&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The average price of a gallon of gas in one city in June [latex]2014[\/latex] was [latex]\\text{\\$3.71}[\/latex]. The average price in that city in July was [latex]\\text{\\$3.64}[\/latex]. Find the percent change.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q516647\">Show Solution<\/span><\/p>\n<div id=\"q516647\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<p><strong>Finding Percent Change<\/strong><br \/>\nFind the Amount of Change: new &#8211; original = 3.64 &#8211; 3.71 = [latex]-[\/latex]$0.07<br \/>\nDivide by the Original Amount: [latex]-[\/latex]0.07\/3.71 =\u00a0 [latex]-[\/latex]0.0188679245<br \/>\nConvert to a Percent and Round: 0.0188679245 x 100 = [latex]-[\/latex]1.9% (or 1.9% decrease)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><span style=\"color: #ff0000;\"><strong>NOTE:\u00a0<span style=\"color: #000000;\">The frame around the answer will turn\u00a0red if the answer entered is wrong.<\/span><\/strong><\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm329600\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=329600&theme=oea&iframe_resize_id=ohm329600&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm329601\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=329601&theme=oea&iframe_resize_id=ohm329601&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to find percent change.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Determine Percent of Change - Increase and Decrease\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/mfe__iO5fbk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-419\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146707, 146706, 146705, 146704, 146703. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Determine Percent of Change - Increase and Decrease. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/mfe__iO5fbk\">https:\/\/youtu.be\/mfe__iO5fbk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":503070,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146707, 146706, 146705, 146704, 146703\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Determine Percent of Change - 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